US8502986B2 - Lightwave interference measurement apparatus that calculates absolute distance using lightwave interference - Google Patents

Lightwave interference measurement apparatus that calculates absolute distance using lightwave interference Download PDF

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US8502986B2
US8502986B2 US13/037,849 US201113037849A US8502986B2 US 8502986 B2 US8502986 B2 US 8502986B2 US 201113037849 A US201113037849 A US 201113037849A US 8502986 B2 US8502986 B2 US 8502986B2
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wavelength
light beam
under test
synthetic
phase
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US20110211198A1 (en
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Yusuke Koda
Yoshiyuki Kuramoto
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Canon Inc
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Canon Inc
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B9/00—Measuring instruments characterised by the use of optical techniques
    • G01B9/02—Interferometers
    • G01B9/02001—Interferometers characterised by controlling or generating intrinsic radiation properties
    • G01B9/02002—Interferometers characterised by controlling or generating intrinsic radiation properties using two or more frequencies
    • G01B9/02004—Interferometers characterised by controlling or generating intrinsic radiation properties using two or more frequencies using frequency scans
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B9/00—Measuring instruments characterised by the use of optical techniques
    • G01B9/02—Interferometers
    • G01B9/02001—Interferometers characterised by controlling or generating intrinsic radiation properties
    • G01B9/02002—Interferometers characterised by controlling or generating intrinsic radiation properties using two or more frequencies
    • G01B9/02003—Interferometers characterised by controlling or generating intrinsic radiation properties using two or more frequencies using beat frequencies
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B9/00—Measuring instruments characterised by the use of optical techniques
    • G01B9/02—Interferometers
    • G01B9/02001—Interferometers characterised by controlling or generating intrinsic radiation properties
    • G01B9/02007—Two or more frequencies or sources used for interferometric measurement
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B9/00—Measuring instruments characterised by the use of optical techniques
    • G01B9/02—Interferometers
    • G01B9/02015—Interferometers characterised by the beam path configuration
    • G01B9/02027—Two or more interferometric channels or interferometers
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B9/00—Measuring instruments characterised by the use of optical techniques
    • G01B9/02—Interferometers
    • G01B9/02055—Reduction or prevention of errors; Testing; Calibration
    • G01B9/02062—Active error reduction, i.e. varying with time
    • G01B9/02067—Active error reduction, i.e. varying with time by electronic control systems, i.e. using feedback acting on optics or light
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B2290/00—Aspects of interferometers not specifically covered by any group under G01B9/02
    • G01B2290/25—Fabry-Perot in interferometer, e.g. etalon, cavity
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B2290/00—Aspects of interferometers not specifically covered by any group under G01B9/02
    • G01B2290/45—Multiple detectors for detecting interferometer signals
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B2290/00—Aspects of interferometers not specifically covered by any group under G01B9/02
    • G01B2290/70—Using polarization in the interferometer

Definitions

  • the present invention relates to a lightwave interference measurement apparatus (interferometer) that measures an absolute distance using lightwave interference.
  • a wavelength-scanning lightwave interference measurement apparatus As a conventional lightwave interference measurement apparatus that measures an absolute distance, a wavelength-scanning lightwave interference measurement apparatus is known.
  • the absolute distance measurement by the wavelength scanning is a low accuracy measurement
  • a method of combining a relative distance measurement by a fixed wavelength with it to improve the accuracy is used.
  • an accuracy of an amount of wavelength scanning, an accuracy of the fixed wavelength, a phase measurement accuracy at the time of measuring the relative distance are main accuracy factors.
  • Japanese Patent No. 2725434 discloses an FM heterodyne method that measures a single interference signal intensity to calculate an absolute distance based on the intensity change of the interference signal that is generated by the wavelength scanning.
  • Japanese Patent No. 2810956 discloses a method of introducing a phase measurement by a Lissajous waveform based on two interference signal intensities having phases different by 90 degrees from each other as a method of a highly-accurate absolute distance measurement compared with the FM heterodyne method.
  • a lightwave interference measurement apparatus includes a wavelength-variable laser configured to periodically perform wavelength scanning between a first reference wavelength ⁇ 1 and a second reference wavelength ⁇ 2 to emit light beam, a wavelength-fixed laser configured to emit light beam having a third reference wavelength ⁇ 3 , a wavelength reference element configured to be able to set a wavelength of the light beam emitted from the wavelength-variable laser to the first reference wavelength ⁇ 1 and the second reference wavelength ⁇ 2 , a light beam splitting element configured to split the light beams emitted from the wavelength-variable laser and the wavelength-fixed laser into reference light beam and light beam under test, a reference surface configured to reflect the reference light beam, a surface under test, configured to reflect the light beam under test, a phase detector configured to detect a phase based on an interference signal of the reference light beam that is reflected on the reference surface and the light beam under test that is reflected on the surface under test, and an analyzer configured to sequentially determine an interference order of the third reference wavelength ⁇ 3 based on the third
  • FIG. 1 is a configuration diagram of a lightwave interference measurement apparatus in a first embodiment.
  • FIGS. 2A to 2C are diagrams illustrating relationships of wavelengths of light sources in a first embodiment.
  • FIG. 3 is a diagram illustrating time changes of wavelengths of light sources in a first embodiment.
  • FIG. 4 is a flowchart of a measurement method in first and second embodiments.
  • FIG. 5 is a conceptual diagram of an interference order M 12 in first and second embodiments.
  • FIG. 6 is a configuration diagram of a lightwave interference measurement apparatus in a second embodiment.
  • FIG. 7 is a diagram illustrating relationships of wavelengths of light sources in a second embodiment.
  • FIG. 8 is a configuration diagram of a phase detecting unit in a second embodiment.
  • FIG. 1 is a configuration diagram of a lightwave interference measurement apparatus 500 in the present embodiment.
  • the lightwave interference measurement apparatus 500 includes a wavelength-variable laser (wavelength-tunable laser) 1 whose wavelengths are periodically scanned and a wavelength-fixed laser 2 whose wavelength is fixed.
  • the wavelength-variable laser 1 periodically performs a wavelength scanning between a first reference wavelength ⁇ 1 and a second reference wavelength ⁇ 2 to emit a light beam.
  • the wavelength-fixed laser 2 emits a light beam of a third reference wavelength ⁇ 3 .
  • the lightwave interference measurement apparatus 500 includes a gas cell 3 as a wavelength reference element, a Fabry-Perot etalon 4 (an etalon) as a wavelength reference element, and a polarizing beam splitter 20 as a light beam splitting element.
  • the wavelength reference element sets the wavelength of the light beam emitted from the wavelength-variable laser 1 to the first reference wavelength ⁇ 1 and the second reference wavelength ⁇ 2 .
  • the light beam splitting element splits each of the light beams emitted from the first reference wavelength ⁇ 1 and the second reference wavelength ⁇ 2 into a reference light beam and a light beam under test.
  • the lightwave interference measurement apparatus 500 includes a reference surface 6 , a surface under test (test surface) 7 , and a detector of a phase of an interference signal based on an optical path difference between the reference surface 6 and the surface under test 7 , i.e. an optical path difference between the reference light beam and the light beam under test.
  • the reference surface 6 and the surface under test 7 are configured to reflect the reference light beam and the light beam under test, respectively.
  • the lightwave interference measurement apparatus 500 also includes an analyzer 8 that calculates an absolute distance between the reference surface 6 and the surface under test 7 .
  • the absolute distance between the reference surface 6 and the surface under test 7 is an absolute position of the surface under test 7 with reference to a position of the reference surface 6 , and is obtained based on the optical path difference between the reference light beam and the light beam under test.
  • the analyzer 8 sequentially determines an interference order of the third reference wavelength ⁇ 3 based on the third reference wavelength ⁇ 3 , synthetic wavelengths ⁇ 12 and ⁇ 13 , an integer component of a phase change amount in the wavelength scanning, and interference orders of the synthetic wavelengths ⁇ 12 and ⁇ 13 , and calculates the absolute distance between the surface under test 7 and the reference surface 6 .
  • the synthetic wavelength ⁇ 12 (a first synthetic wavelength) is represented by ⁇ 1 ⁇ 2 /
  • the synthetic wavelength ⁇ 13 (a second synthetic wavelength) is represented by ⁇ 1 ⁇ 3 /
  • the lightwave interference measurement apparatus 500 connects the two synthetic wavelengths generated from the wavelength-variable laser 1 whose wavelengths are periodically scanned and the wavelength-fixed laser 2 to be able to determine an interference order. Therefore, an amount of wavelength scanning of the wavelength-variable laser 1 is significantly reduced. Thus, the wavelength scanning by a current modulation of the laser can be performed, and a high-speed absolute length measurement is realized.
  • the light beam emitted from the wavelength-variable laser 1 is split by a beam splitter 5 .
  • the light beam emitted from the wavelength-fixed laser 2 that has a wavelength different from that of the wavelength-variable laser 1 also enters the beam splitter 5 , and the light beam is also split when its ray axis becomes coaxial with reference to that of the wavelength-variable laser 1 .
  • One of the light beams split by the beam splitter 5 transmits through the Fabry-Perot etalon 4 , and then it is separated by a spectral element 12 into light beams of the wavelength-variable laser 1 and the wavelength-fixed laser 2 .
  • the amount of light transmitted through the Fabry-Perot etalon 4 is detected by a detector 13 a for the light beam of the wavelength-variable laser 1 and by a detector 13 b for the light beam of the wavelength-fixed laser 2 .
  • the emission light beam of the wavelength-fixed laser 2 enters the gas cell 3 .
  • the same type of DFB laser diode is used as each of the wavelength-variable laser 1 and the wavelength-fixed laser 2 .
  • the wavelength-variable laser 1 and the wavelength-fixed laser 2 are provided separately from each other, a plurality of laser diodes may also be integrated as one element similarly to a multiwavelength light source used for an optical communication. In this case, it is advantageous in view of the cost and the size.
  • an amount of transmitted light is detected by a detector 15 .
  • acethylene is used as the gas cell 3 which is used along with the wavelength-variable laser 1 having a wavelength of near 1.5 ⁇ m.
  • the wavelength-variable laser 1 having a wavelength of near 1.5 ⁇ m.
  • carbon monoxide, hydrogen cyanide, or the like is used as another inclusion gas that is usable in a wavelength range near 1.5 ⁇ m. Since each gas has a different wavelength range and different central wavelength accuracy, it may be selected as necessary.
  • FIG. 2A illustrates a transmission spectrum of the gas cell 3
  • FIG. 2B illustrates a transmission spectrum of the Fabry-Perot etalon 4
  • FIG. 2C illustrates spectra of the wavelength-variable laser 1 and the wavelength-fixed laser 2 .
  • a wavelength control apparatus 14 controls the wavelength of the wavelength-fixed laser 2 so as to be stabilized to the third reference wavelength ⁇ 3 that is an absorption line of the gas cell 3 using a single of the detector 15 .
  • the wavelength control apparatus 14 controls the optical path length of the Fabry-Perot etalon 4 so that the transmission spectrum of the Fabry-Perot etalon 4 becomes equal to the third reference wavelength ⁇ 3 using the signal of the detector 13 b .
  • an absolute value of the wavelength of the transmission spectrum of the Fabry-Perot etalon 4 needs to be guaranteed.
  • the Fabry-Perot etalon 4 has a periodical transmission property at an equivalent frequency interval FSR, and as described above, the absolute value of its vacuum wavelength is guaranteed.
  • One of the transmission spectra of the Fabry-Perot etalon 4 is used as the first reference wavelength ⁇ 1 .
  • the stabilization of the wavelength is performed by adjusting the wavelength of the wavelength-variable laser 1 by the wavelength control apparatus 14 so that the transmission intensity of the detector 13 a becomes constant.
  • the amount of incident light is also detected to be corrected.
  • a method of modulating injection current is used as a method of adjusting the wavelength.
  • the wavelength-variable laser 1 is stabilized to the transmission spectrum of the Fabry-Perot etalon 4 which corresponds to the first reference wavelength ⁇ 1 .
  • the wavelength scanning to the second reference wavelength ⁇ 2 is performed by the current modulation to stabilize the wavelength of the wavelength-variable laser 1 to the second reference wavelength ⁇ 2 .
  • the wavelength scanning from the second reference wavelength ⁇ 2 to the first reference wavelength ⁇ 1 is stabilized to one of at least two reference wavelengths, i.e. the first reference wavelength ⁇ 1 and the second reference wavelength ⁇ 2 .
  • the wavelength-variable laser 1 also periodically performs a scanning between the first reference wavelength ⁇ 1 and the second reference wavelength ⁇ 2 at high speed.
  • FIG. 3 illustrates a time change of each wavelength of the wavelength-variable laser 1 and the wavelength-fixed laser 2 in the present embodiment.
  • the wavelength-variable laser 1 has a first time period (0 ⁇ t ⁇ t 0 ) in which the wavelength is stabilized to the first reference wavelength ⁇ 1 and a second time period (t 1 ⁇ t ⁇ t 0 ′) in which the wavelength is stabilized to the second reference wavelength ⁇ 2 .
  • the Fabry-Perot etalon 4 is used in addition to the gas cell 3 to improve the accuracy of the reference wavelength, only the gas cell 3 may be used if an accuracy condition for determining the order is met as described below.
  • the maximum value of ⁇ needed in Expression (2) is around 1.5 m, and when it is converted into a wavelength difference of the second reference wavelength ⁇ 2 and the first reference wavelength ⁇ 1 , i.e. an amount of wavelength scanning, the amount of wavelength scanning becomes an extremely small value of 1.5 ⁇ m.
  • a temperature modulation is necessary and there is a problem that it takes time to perform the wavelength scanning.
  • the amount of wavelength scanning is reduced as described above, a high-speed scanning can be realized by the current modulation. If another wavelength-fixed laser that is different from the wavelength-fixed laser 2 is added, the amount of wavelength scanning of the wavelength-variable laser can be further reduced.
  • the other light beam split by the beam splitter 5 is further split by a beam splitter 18 .
  • One of the light beams split by the beam splitter 18 (a first light beam) travels to a polarizing beam splitter 19 .
  • the other split light beam (a second light beam) enters a wavelength shifter 11 .
  • the wavelength shifter 11 applies a predetermined amount of frequency shift d ⁇ for an incident wavelength using an acousto-optic element (not shown) with respect to the light beam outputted from each of the wavelength-variable laser 1 and the wavelength-fixed laser 2 .
  • the wavelength shifter 11 rotates the polarized light by 90 degrees using a wave plate (not shown) to emit polarized light orthogonal to the incident polarized light.
  • the light beam emitted from the wavelength shifter 11 travels to the polarizing beam splitter 19 . After the first light beam and the second light beam are changed to have a common optical path again by the polarizing beam splitter 19 , it is diverged by a beam splitter 21 into two paths.
  • the spectral element 17 separates the light beams of the wavelength-variable laser 1 and the wavelength-fixed laser 2 entering it at the same axis.
  • An arrayed waveguide grating is used as the spectral element 17 .
  • the present embodiment is not limited to this, and a prism or a bulk diffraction grating can also be used and it may be selected considering required wavelength resolution and cost.
  • a beat signal corresponding to a frequency difference of both the light beams is detected by a phase detector 10 b .
  • a beat signal corresponding to a frequency difference of both the light beams is detected by a phase detector 10 a .
  • the interference signal of the first light beam and the second light beam is obtained by extracting a common polarization component of the first light beam and the second light beam using a polarizer in each of the phase detectors 10 a and 10 b .
  • each of the interference signals detected by the phase detectors 10 a and 10 b via the spectral element 17 is referred to as a reference signal.
  • the other light beam diverged by the beam splitter 21 enters a distance measuring interferometer 100 .
  • a polarizing beam splitter 20 in the distance measuring interferometer 100 is configured so as to transmit the first light beam and reflect the second light beam.
  • the second light beam reflected by the polarizing beam splitter 20 is reflected on the reference surface 6 , and enters a spectral element 16 after it is reflected by the polarizing beam splitter 20 .
  • the first light beam transmitted through the polarizing beam splitter 20 is reflected on the surface under test 7 , and enters the spectral element 16 after it transmits through the polarizing beam splitter 20 .
  • the light beam reflected on the reference surface 6 is referred to as a reference light beam
  • the light beam reflected on the surface under test 7 is referred to as a light beam under test.
  • the interference signal of the reference light beam and the light beam under test, which has the first reference wavelength ⁇ 1 , is detected by the phase detector 10 b .
  • the interference signal of the reference light beam and the light beam under test, which has the third reference wavelength ⁇ 3 is detected by the phase detector 10 a .
  • each of the phase detectors 10 a and 10 b (a phase detecting portion) detects a phase based on the interference signal of the reference light beam reflected on the reference surface 6 and the light beam under test, reflected on the surface under test 7 .
  • each of the interference signals detected by the phase detectors 10 a and 10 b via the spectral element 16 is referred to as a measured signal.
  • the measured signal is the same as the reference signal in that it is a beat signal corresponding to a frequency difference between both the light beams as the interference signal of the first light beam and the second light beam, but the phase of the interference signal is different from the phase of the reference signal depending on the optical path length difference of the light beam under test and the reference light beam.
  • the polarizing beam splitter 20 that is capable of splitting the polarization components is used as a light beam splitting element of the distance measuring interferometer 100 to be able to separate the light beams that are reflected on the reference surface 6 and the surface under test 7 respectively by the polarization. Therefore, a heterodyne detection between the surface under test 7 and the reference surface 6 can be performed by adding a slight frequency shift difference between the two polarized lights orthogonal to each other, and a highly-accurate phase measurement can be realized.
  • the polarizing beam splitter 20 is used as the light beam splitting element of the distance measuring interferometer 100 , but the present embodiment is not limited to this and a non-polarizing beam splitter may also be used.
  • a ⁇ /8 plate is disposed between the non-polarizing beam splitter and the reference surface 6 , and the intensity of each polarization component is detected via the polarizing beam splitter after the reflected light beam on the reference surface 6 and the reflected light beam on the surface under test 7 are superimposed again.
  • the phases of the detected two interference signals are shifted by 0 degree and 90 degrees, respectively.
  • the phase measurement may be performed based on these two interference signals. In this case, since the phase measurement accuracy is reduced although it is easily configured, for example it is necessary to enlarge the amount of wavelength scanning based on Expressions (1) and (2).
  • an environment measurement unit 9 that determines an atmospheric refractive index near the surface under test 7 is disposed near the surface under test 7 .
  • the environment measurement unit 9 is configured by including measurement sensors of atmospheric temperature and atmospheric pressure.
  • the temperature sensitivity of the atmospheric refractive index is 1 ppm/deg C. and the atmospheric pressure sensitivity is 0.3 ppm/hPa, and the refractive index of around 0.1 ppm can be easily ensured even if a relatively inexpensive thermometer or barometer is used.
  • the measured wavelength is corrected based on the atmospheric refractive index measured by the environment measurement unit 9 , but the measurement of the refractive index is not necessary when the atmospheric wavelength is controlled by using an etalon or the like of an air gap that is disposed near the environment measurement unit 9 .
  • the analyzer 8 inputs the reference signal, the measured signal, and the signal from the environment measurement unit 9 , and calculates an absolute distance between the surface under test 7 and the reference surface 6 , i.e. an optical path difference of the light beam under test and the reference light beam. Furthermore, the analyzer 8 is coupled to the wavelength control apparatus 14 , and performs the wavelength control of the wavelength-variable laser 1 in accordance with a measurement flow. In the present embodiment, when a plurality of distance measuring interferometers 100 are disposed for one light source unit 200 , it can be easily applied by splitting light beams between the light source unit 200 and the beam splitter 18 .
  • FIG. 4 is a flow chart of the measurement method in the present embodiment.
  • the flow is roughly divided into two loops.
  • One is a wavelength control loop, and the other is a measurement loop.
  • the wavelength control loop is performed based on instructions of the wavelength control apparatus 14 .
  • the measurement loop is performed based on instructions of the analyzer 8 .
  • a flow that performs a relative length measurement at high speed in Steps S 101 to S 105 and a flow that performs an absolute length measurement in Steps S 101 to S 103 , S 110 to S 112 , and S 105 are included.
  • the wavelength-variable laser 1 is scanned between the first reference wavelength ⁇ 1 and the second reference wavelength ⁇ 2 (Steps S 401 and S 403 ), and then the stabilized control is repeatedly performed so that the wavelength is stabilized to one of the reference wavelengths (Steps S 402 , S 404 ).
  • Steps 402 and S 404 after the control to the reference wavelength is completed, a wavelength scanning completion flag is sent to Step S 103 at the measurement loop side.
  • Step S 103 receiving the wavelength scanning completion flag, it is determined whether the wavelength scanning is completed.
  • Step S 101 the phase measurement is performed in the first reference wavelength ⁇ 1 and the third reference wavelength ⁇ 3 .
  • Step S 301 the environment measurement is performed.
  • an environment measurement result of the atmosphere of the light beam under test from the environment measurement unit 9 is loaded by the analyzer 8 .
  • the humidity of the optical path under test is guaranteed, and the atmospheric temperature t and the atmospheric pressure p are measured as the environment measurement.
  • the phase measurement means that the phase difference between the measured signal and the reference signal is measured, and is obtained by measuring the phases of the reference signal and the measured signal by a phase meter in the analyzer 8 to calculate the difference.
  • a phase connection is performed for the measured phase, and it continuously changes with respect to the time.
  • an optical path length difference between the light beam under test and the reference light beam from the emission of the wavelength-variable laser 1 to the polarizing beam splitter 19 is defined as L 1
  • an optical path length difference of the light beam under test and the reference light beam from the polarizing beam splitter 19 to the phase detector 10 a or the phase detector 10 b is defined as 2n( ⁇ )D.
  • n( ⁇ ) denotes a refractive index of the optical path of the light beam under test
  • D denotes an absolute distance between the reference surface and the surface under test.
  • I ref I 0 ⁇ cos ⁇ ( 2 ⁇ ⁇ ⁇ ( dvt + L 1 ⁇ 11 ) )
  • I test I 0 ⁇ cos ⁇ ( 2 ⁇ ⁇ ⁇ ( dvt + L 1 ⁇ 11 + 2 ⁇ ⁇ n ⁇ ( ⁇ 11 ) ⁇ D ⁇ 11 ) ) ( 3 )
  • ⁇ ⁇ ( t ) 2 ⁇ ⁇ ⁇ 2 ⁇ ⁇ n ⁇ ( ⁇ ⁇ ( t ) ) ⁇ D ⁇ ( t ) ⁇ ⁇ ( t ) ( 4 )
  • a phase ⁇ a (t 0 ) of the wavelength-variable laser 1 that are measured in Step S 201 is represented by Expression (6).
  • the wavelength of the wavelength-variable laser 1 is the first reference wavelength ⁇ 1 at the time t 0 .
  • “mod(u, k)” means a remainder of a first argument for a second argument k.
  • a phase ⁇ 3 (t 0 ) that is measured in Step S 101 is represented by Expression (8).
  • the wavelength of the wavelength-fixed laser 2 is always the third reference wavelength ⁇ 3 .
  • Steps S 101 and S 201 The histories of the phase measurement results obtained in Steps S 101 and S 201 are stored in Steps S 102 and S 202 , respectively.
  • Step S 103 based on the wavelength scanning completion flag sent from Steps S 402 and S 404 of the wavelength control loop, it is determined whether the wavelength scanning is completed. The flow proceeds to Step S 104 when the wavelength scanning is not completed yet, and on the other hand, the flow proceeds to Step S 110 when the wavelength scanning is completed.
  • Step S 104 based on the measurement result of the phase connection in Step 5102, an interference order N 3 is calculated by Expression (9) using an interference order N 3 (i) and a phase measurement result 3 (i) at the time of the previous measurement and a current phase measurement result ⁇ 3 (i+1).
  • N 3 ( i+ 1) N 3 ( i )+round( ⁇ 3 ( i+ 1) ⁇ 3 ( i )) (9)
  • Step S 105 the analyzer 8 calculates the absolute distance D using the relative phase change of the third reference wavelength ⁇ 3 and the atmospheric wavelength corrected based on the environment measurement result in Step S 301 .
  • the analyzer 8 calculates the absolute distance D using the high-speed relative length measurement and the interference order N 3 until the flag of the completion of the next wavelength scanning is confirmed. Then, the flow returns to the beginning of the measurement loop.
  • Step S 110 the changes of a position of the surface under test at the time of measuring the phase of the two synthetic wavelengths and at the time of measuring the phase change amount in the wavelength scanning are corrected using the calculation result of the relative displacement of the third reference wavelength ⁇ 3 .
  • the relative displacement of the surface under test 7 is calculated based on the phase change of the third reference wavelength ⁇ 3 in the wavelength scanning, and the interference orders of the synthetic wavelengths ⁇ 12 and ⁇ 13 are corrected so as not to be influenced by the relative displacement of the surface under test 7 .
  • the phase of the wavelength-variable laser 1 at the time t 1 is obtained by Expression (10).
  • phase ⁇ 3 (t 1 ) of the wavelength-fixed laser 2 at the time t 1 is represented by Expression (12).
  • the analyzer 8 calculates the absolute distance D at the time t 1 using this phase result.
  • the relative displacement ⁇ D(t 0 ⁇ t 1 ) is calculated by Expression (13) based on the continuous phase changes between the times t 0 to t 1 .
  • ⁇ ⁇ ⁇ D ⁇ ( t 0 ⁇ t 1 ) ⁇ 3 4 ⁇ ⁇ ⁇ ⁇ n ⁇ ( ⁇ 3 ) ⁇ ( ⁇ 3 ⁇ ( t 1 ) - ⁇ 3 ⁇ ( t 0 ) ) ( 13 )
  • the phase ⁇ a (t 0 ), i.e. the measurement phase result, that is stored as a history in Step S 202 is corrected to a phase ⁇ ′ a (t 1 ) in the absolute distance D(t 1 ) using Expression (14) in a state where the first reference wavelength ⁇ 1 is maintained.
  • ⁇ a ′ ⁇ ( t 1 ) 2 ⁇ ⁇ ⁇ mod ( ⁇ a ⁇ ( t 0 ) 2 ⁇ ⁇ + 2 ⁇ ⁇ n ⁇ ( ⁇ 1 ) ⁇ 1 ⁇ ⁇ ⁇ ⁇ D ⁇ ( t 0 ⁇ t 1 ) , 1 ) ( 14 )
  • Step S 111 an interference order M 12 (t 1 ) of the absolute distance Dat the measurement time t 1 is calculated.
  • FIG. 5 is a conceptual diagram of the interference order M 12 in the present embodiment.
  • the interference order M 12 is calculated by subtracting the integer component of the phase ⁇ a (t 0 ) at the time t 0 from the integer component of the phase ⁇ a (t 1 ) at the time t 1 .
  • the absolute distance D is different depending on each time when the surface under test varies, the phase change caused by the variation of the surface under test is contained in the interference order M 12 . Therefore, when the wavelength scanning is performed between the first reference wavelength ⁇ 1 and the second reference wavelength ⁇ 2 , the interference order M 12 (t) is calculated by using a correction expression represented by Expression (15).
  • the interference order M 12 (t 1 ) is represented by Expression (16).
  • ⁇ 12 is a synthetic wavelength of the first reference wavelength ⁇ 1 and the second reference wavelength ⁇ 2
  • n g ( ⁇ 1 , ⁇ 2 ) denotes a group refractive index for the first reference wavelength ⁇ 1 and the second reference wavelength ⁇ 2 .
  • Step S 112 an interference order N 3 (t 1 ) of the interference measurement by the third reference wavelength ⁇ 3 is calculated.
  • a first absolute distance D(t 1 ) is calculated by Expression (17) using the synthetic wavelength ⁇ 12 .
  • Step S 105 the atmospheric refractive index and the absolute distance D are calculated in Step S 105 .
  • the atmospheric refractive index n of the dry air is calculated by Expression (21) of Edlen based on the temperature t [deg C.] and the pressure p [Pa].
  • the environment measurement unit 9 is used as a refractive index measuring portion in the present embodiment, the present embodiment is not limited to this and for example a refractive index measuring interferometer may also be used.
  • the refractive index measuring interferometer calculates a refractive index based on an interference signal generated by an optical path difference of an atmospheric reference optical path that has an atmospheric optical path that has the same length as that of a vacuum reference optical path.
  • the absolute distance D(t 1 ) in Step S 105 is calculated by Expression (22).
  • phases of the first reference wavelength ⁇ 1 , the second reference wavelength ⁇ 2 , and the third reference wavelength ⁇ 3 are defined as ⁇ 1 , ⁇ 2 , and ⁇ 3 , respectively.
  • the atmospheric refractive indexes for the third reference wavelength ⁇ 3 , the first synthetic wavelength ⁇ 12 , and the second synthetic wavelength ⁇ 13 are defined as n( ⁇ 3 ), n g ( ⁇ 1 , ⁇ 2 ), and n g ( ⁇ 1 , ⁇ 3 ), respectively.
  • the flow in which the absolute distance at the time t 1 is calculated based on the phase measurement result between the times t 0 to t 1 (the wavelength scanning of ⁇ 1 to ⁇ 2 ) illustrated in FIG. 3 is described.
  • the present embodiment is not limited to this, and similarly the absolute distance at the time t 1 ′ can also be calculated using the phase measurement result between the time t 0 ′ to t 1 ′ (the wavelength scanning of ⁇ 2 to ⁇ 1 )
  • the absolute length measurement can be always performed by periodically scanning the wavelength of the wavelength-variable laser at high speed. Therefore, according to the present embodiment, the amount of wavelength scanning can be reduced and the lightwave interference measurement apparatus capable of performing a high-speed absolute distance measurement in an easy configuration can be provided.
  • FIG. 6 is a configuration diagram of a lightwave interference measurement apparatus 600 in the present embodiment.
  • the present embodiment is different from the first embodiment in that a wavelength-variable laser 31 in which a frequency offset lock is performed with reference to the wavelength-fixed laser 30 is used instead of the wavelength-variable laser 1 in the first embodiment and that a homodyne method is used as a phase detection method.
  • the wavelength-fixed laser 30 is a frequency-stabilized light source, and functions as a wavelength reference element of the wavelength-variable laser 31 .
  • a light beam emitted from the wavelength-fixed laser 30 is split by a beam splitter 35 .
  • a light beam emitted from the wavelength-fixed laser 2 that has a wavelength different from the wavelength of the wavelength-fixed laser 30 also enters the beam splitter 35 , and the light beam is also split when its ray axis becomes coaxial with reference to that of the wavelength-variable laser 30 .
  • One of the light beams split by the beam splitter 35 transmits through the Fabry-Perot etalon 4 , and then it is separated by the spectral element 12 into light beams of the wavelength-fixed laser 30 and the wavelength-fixed laser 2 .
  • An amount of light after transmitting through the Fabry-Perot etalon 4 is detected by a detector 13 a for the light beam of the wavelength-fixed laser 30 and by a detector 13 b for the light beam of the wavelength-fixed laser 2 .
  • the other light beam split by the beam splitter 35 travels to a polarizing beam splitter 22 , and the light beam of the wavelength-fixed laser 30 transmits through the polarizing beam splitter 22 to enter a detector 23 .
  • the light beam of the wavelength-fixed laser 2 is reflected on the polarizing beam splitter 22 , and then it enters a distance measuring interferometer 100 .
  • the light beam emitted from the wavelength-variable laser 31 also enters the polarizing beam splitter 22 , and the light beam is also split when its ray axis becomes coaxial with reference to that of the wavelength-variable laser 30 .
  • First light beam of the split light beams enters the detector 23 , and second light beam of them enters the distance measuring interferometer 100 .
  • the detector 23 detects a beat signal that corresponds to a frequency of a difference of the wavelength-variable laser 31 and the wavelength-fixed laser 30 .
  • the phase of the beam signal is compared with a phase of a signal from a frequency synthesizer 34 that outputs a known frequency signal using a phase detector in the wavelength control apparatus 33 . Then, the frequency of the wavelength-variable laser 31 is stabilized to a frequency that is obtained by offsetting the frequency of the frequency synthesizer 34 to the frequency of the wavelength-fixed laser 30 .
  • the wavelength of the wavelength-variable laser 31 is also scanned following it.
  • the wavelength-variable laser 31 can be freely stabilized between the first reference wavelength ⁇ 1 and the second reference wavelength ⁇ 2 , and it periodically scans between these wavelengths (between ⁇ 1 and ⁇ 2 ) at high speed.
  • FIG. 7 is a diagram illustrating a transmission spectrum of the gas cell 3 and spectra of the wavelength-variable laser 31 , the wavelength-fixed laser 30 , and the wavelength-fixed laser 2 .
  • the emission light beam of the wavelength-fixed laser 2 enters the gas cell 3 , and it is stabilized to the third reference wavelength ⁇ 3 .
  • the emission light beam of the wavelength-fixed laser 30 also enters the gas cell 3 , and it is stabilized to a transmission spectrum that corresponds to a wavelength shorter than the first reference wavelength ⁇ 1 .
  • phase detecting unit 32 a and 32 b a phase detector
  • the phase detecting unit 32 a detects an interference phase by the optical path difference between a reference optical path and an optical path under test in the first reference wavelength ⁇ 1 via the spectral element 16 .
  • the phase detecting unit 32 b detects an interference phase by the optical path difference between the reference optical path and the optical path under test in the second reference wavelength ⁇ 2 .
  • the polarizing beam splitter 20 is used as a light beam separating element of the distance measuring interferometer 100 also in the present embodiment, the light beams reflected on the reference surface 6 and the surface under test 7 respectively can be separated by the polarization. Therefore, homodyne detection by the phase different control using the polarization difference can be performed, and highly-accurate phase detection can be realized.
  • FIG. 8 is a configuration diagram of the phase detecting units 32 a and 32 b .
  • the phase detecting unit 32 a and 32 b convert the polarizations of the light beam under test and the reference light beam into a clockwise circular polarization and a counterclockwise circular polarization by using a ⁇ /4 plate 41 having a fast axis that is 45 degrees with reference to a polarizing axis angle of the light beam under test and the reference light beam.
  • the light beam after the polarization conversion is split by a grating beam splitter 42 into three light beams of 0th and ⁇ 1st order diffracted lights that have an equivalent amount of light.
  • the three split light beams transmit through a polarizer array 43 that is disposed so that an angle of the transmission polarized light is different from each of the light beams, and an amount of interference signal light of each of three polarization directions is detected by detectors 50 a , 50 b, and 50 c .
  • each of the polarizers of the polarizer array 43 is arranged at an angle having a pitch of 120 degrees, amounts of lights I a , I b , and I c that are obtained by the detectors 50 a , 50 b , and 50 c are represented by Expression (23).
  • ⁇ is a phase difference of the interference signal caused by the optical path length difference between the light beam under test and the reference light beam.
  • the phase difference ⁇ is calculated using Expression (24).
  • the phase detecting units 32 a and 32 b are coupled to the analyzer 8 .
  • the analyzer 8 detects a phase depending on the optical path lengths of the light beams under test and the reference light beam in the first reference wavelength ⁇ 1 and a phase depending on the optical path lengths of the light beam under test and the reference light beam in the third reference wavelength ⁇ 3 using Expression (24) based on the result of detecting the amounts of lights.
  • the phase detecting units 32 a and 32 b in the present embodiment detects the interference signal intensity in three known phase differences in the configuration illustrated in FIG. 8 , but the interference signal intensity in a plurality of known phase differences may also be detected in another configuration.
  • the phase detecting unit may also be configured so as to generate a tilt stripe between the light beam under test and the reference light beam using a prism having a birefringence to detect the amount of light by spatially generating a phase difference.
  • the number of the known phase differences or the interval of the known phase differences are not limited as described above, and it maybe appropriately selected in accordance with required accuracy.
  • an inexpensive detection system can be configured compared with that of the heterodyne detection of the first embodiment.
  • the performance of around 10 ⁇ 4 [wave] that is similar to that of the heterodyne detection can be realized by correcting characteristics of the gains, the offsets, and the phases of the detectors 50 a , 50 b , and 50 c .
  • the environment measurement unit 9 to determine the atmospheric refractive index near the surface under test is disposed near the surface under test 7 .
  • the measurement method of the present embodiment is the same as that of the first embodiment, and therefore the description of the method is omitted.

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  • Optics & Photonics (AREA)
  • Instruments For Measurement Of Length By Optical Means (AREA)
  • Length Measuring Devices By Optical Means (AREA)
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